Your friend is probably not really lying, at least not primarily to you. This sounds like a case of her not being truthful to herself first and foremost. I would assume that she would honestly like the things she says to you to be true (that she's not into relationships right now, that the thing with her ex is over, etc.), but evidently they are not. In other words, she probably believes what she tells you when she tells it to you - but then things change when he texts or calls.
If you want to be her friend, the best thing you can do is probably to have an honest conversation about what is going on in her love life. Happy people typically don't flip-flop between "I am so over this" and "he is coming to my place in an hour so you need to get out". What you can do as a friend is help her come to understand her own emotions - maybe, even likely, she isn't quite over this guy, and that's fine, but she should understand how she feels so that she can make informed decisions. As Legisey says, it's important to not judge her for her emotions (it's ok to still have feelings for somebody, even if these feelings led her to heartbreak before), but that does not necessarily mean that the best course of action is to jump right back into a relationship. Alternating between "I hate that guy" and one-night stands is probably even worse. These are things that you as a friend can help her talk through (but keep in mind that at the end of the day it's not about you - if she tells you she will not see him again only to hook up with him the next day, she isn't doing this to spite you!).
Of course, there is also the alternate possibility that, at least from her side, your relationship isn't quite platonic, and that's why she wants to convince you that she is in fact single and (almost) available. We random people on the Internet can't figure this out for you, but it's certainly a possibility to consider if she does not want to talk about her ex to specifically you.